Problem
Change the total and every share changes
A circle graph gives the shares of marbles by color, and one color's count is known. After that color is given away, we need what percent of the rest is red.
Data & probabilityRatios
Your answer
How to solve
Strategy Work Backwards — Percentages are useless until we know what they are percentages of, so turn the graph into counts first. Then remove the yellow marbles and work the percent out again -- against the new, smaller total.
1STEP 1
Find the yellow share
The four slices fill the whole circle, so their percentages add to 100.
100 - 40 - 30 - 10 = 20
Yellow is 20%.
6.SP.B.4Analyze The Units2STEP 2
Turn a share back into the total
The 10 yellow marbles are that 20%, so 10 is one fifth of all the marbles.
10 ÷ 20 × 100 = 50
Junseo has 50 marbles.
6.RP.A.3Work Backwards3STEP 3
Count the red marbles
Red is 40% of those 50 marbles.
50 × 0.4 = 20
There are 20 red marbles.
6.RP.A.3Organize Information In More Ways4STEP 4
Take the yellow ones away and re-divide
Giving away 10 marbles leaves 40, and the red ones are untouched, so divide 20 by the new total.
50 - 10 = 40, 20 ÷ 40 = 0.5
Red is now half of what is left, or 50%.
6.RP.A.3Organize Information In More WaysRed's share rises even though no red marble was touched.
Why?
A share is the count measured against the total, so it can change when either of the two changes.
🧱One-to-one correspondenceIf each thing here pairs with exactly one thing there, the two groups are the same size.
Why?
Giving the yellow marbles away removes them from the total but leaves the red count alone, so the same twenty reds are now measured against a smaller whole.
🧱Whole is the sum of its partsBreak a thing into pieces with no gaps or overlaps and the pieces add back to the whole.
Answer
50%
Count it out: 20 red, 15 blue and 5 purple make 40 marbles, and 20 of those 40 are red.
Takeaway
A share can change without the count changing -- when the total shrinks, every remaining share grows.
- Find the yellow share
- Turn a share back into the total
- Count the red marbles
- Take the yellow ones away and re-divide